MHB Radians to Degrees, Minutes, Seconds

AI Thread Summary
The discussion focuses on converting radians to degrees, minutes, and seconds, specifically for the values 0.47623 and 0.25412. The conversion process for 0.47623 is detailed, starting with calculating the degree equivalent using the formula 0.47623 × (180°/π), resulting in approximately 27.29°. This is further broken down into degrees, minutes, and seconds, yielding a final result of approximately 27° 17' 9.49''. Participants express curiosity about potentially easier methods for such conversions, while acknowledging the straightforwardness of the presented manual approach. The conversation highlights the balance between manual calculations and the use of technology for conversions.
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Reduce the following numbers of radians to degrees, minutes, and seconds.

(a). 0.47623.

(b). 0.25412.

Can someone work out (a) in steps? I can then use it as a guide to solve (b).
 
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Okay, here is how I would work a):

First, let's get a decimal approximation for the number of degrees, with a good amount of precision:

$$0.47623\cdot\frac{180^{\circ}}{\pi}=\frac{85.7214}{\pi}^{\circ}\approx27.285969077515198^{\circ}$$

Okay, now we think of this as:

$$0.47623\approx27^{\circ}+0.285969077515198^{\circ}\cdot\frac{60'}{1^{\circ}}\approx27^{\circ}+17.15814465091188'$$

Continuing:

$$0.47623\approx27^{\circ}+17' + 0.15814465091188'\cdot\frac{60''}{1'}\approx27^{\circ}+17'+9.4886790547128''$$

Using standard notation and rounding some, we may write:

$$0.47623\approx27^{\circ}17'9.49''$$
 
MarkFL said:
Okay, here is how I would work a):

First, let's get a decimal approximation for the number of degrees, with a good amount of precision:

$$0.47623\cdot\frac{180^{\circ}}{\pi}=\frac{85.7214}{\pi}^{\circ}\approx27.285969077515198^{\circ}$$

Okay, now we think of this as:

$$0.47623\approx27^{\circ}+0.285969077515198^{\circ}\cdot\frac{60'}{1^{\circ}}\approx27^{\circ}+17.15814465091188'$$

Continuing:

$$0.47623\approx27^{\circ}+17' + 0.15814465091188'\cdot\frac{60''}{1'}\approx27^{\circ}+17'+9.4886790547128''$$

Using standard notation and rounding some, we may write:

$$0.47623\approx27^{\circ}17'9.49''$$

There's got to be an easier way to do this, right?
 
RTCNTC said:
There's got to be an easier way to do this, right?

There could be, but that's the most straightforward way I know to do such a conversion by hand (i.e. without using a calculator programmed to do such conversions).
 
MarkFL said:
There could be, but that's the most straightforward way I know to do such a conversion by hand (i.e. without using a calculator programmed to do such conversions).

I recall watching a high school teacher on youtube.com using a totally different method.
 
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